Question

Suppose we want to test whether or not three means are equal. We want to perform this test with a 4% significance level.

If we perform an ANOVA test, what is the probability of the test producing accurate results (avoiding a Type I error)?

Suppose we, instead, run three separate hypothesis tests (t-tests), each with 4% significance level.

• Mean 1 = Mean 2
• Mean 1 = Mean 3
• Mean 2 = Mean 3

What is the probability that all three tests would be accurate? Hint: use principles of probability to help your calculations: P(accurate AND accurate AND accurate)  (Write your answer accurate without rounding.)

Why would we use ANOVA instead of three separate tests?

Why would we want to use three separate tests instead of ANOVA?

Answer 1

In Anova

The probability of the test producing accurate results (avoiding a Type I error)?

= 1 - 0.04

=0.96

Suppose, We instead run three separate hypothesis tests

(t-tests), each with 4% significance level.

What is the probability that all three tests would be accurate? = (1 -0.04)^3

=(0.96)^3

=0.884736

since 0.96 > 0.884736

we should use ANOVA instead of three separate tests

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Thank